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DIAHEMITONIC MODALITY: A QUARTER-TONAL COMPOSITION SYSTEM

Published online by Cambridge University Press:  01 September 2023

Simon Kaplan
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Abstract

This article describes a design process for a composition system based upon the quarter-tone scale. As the semitone and quarter-tone scales share the same properties, a musical grammar based upon the former is used as a model to construct an analogous musical grammar based upon the latter. Within the scope of diatonic modal music, the organisation of pitches and durations is analysed from a scientific perspective. Several parameters are taken into consideration: scale, mode, chord, cadence, metre and rhythm. The one-to-one mapping of each facet of diatonic modality onto quarter-tonality results in diahemitonic modality.

Type
RESEARCH ARTICLE
Information
Tempo , Volume 77 , Issue 306 , October 2023 , pp. 69 - 92
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

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References

1 Coined from the ancient Greek diahemitonikos, meaning ‘of semitones passed through (the heptachords)’ (from dia, ‘through’, + hemisys, ‘half’, + tonos, ‘tone’, + -ikos, ‘-ic’), upon the model of ‘diatonic’.

2 Coined from the ancient Greek hendekatonikos, meaning ‘of 11 tones’ (from hendeka, ‘11’, + tonos, ‘tone’, + -ikos, ‘-ic’), upon the model of ‘pentatonic’.

3 Wyschnegradsky, Ivan, Manual of Quarter-Tone Harmony, tr. Kaplan, Rosalie (New York: Underwolf, 2017), pp. 19–23Google Scholar.

4 Jedrzejewski, Franck, Dictionnaire des musiques microtonales, new revised and expanded edition (Paris: L'Harmattan, 2014), pp. 60–62Google Scholar.

5 d'Indy, Vincent, Cours de composition musicale, premier livre (Paris: Durand, 1912), pp. 91–106Google Scholar.

6 Ruland, Heiner, Expanding Tonal Awareness: A Musical Exploration of the Evolution of Consciousness – from Ancient Tone Systems to New Tonalities – Guided by the Monochord, tr. Logan, John F. (Forest Row: Rudolf Steiner, 2014), pp. 44–46Google Scholar.

7 Cowell, Henry, New Musical Resources (New York: Alfred A. Knopf, 1930; New York: Cambridge University Press, 1996), pp. 45–81Google Scholar. This reference is to the Cambridge edition.

8 Coined from the Latin octansdesesquialter, meaning ‘(in the ratio) of (one) and three-eighths (elements) to the other’ (from octans, ‘eighth’, + de, ‘off’, + semis, ‘half’, + -que, ‘and’, + alter, ‘other’), upon the model of ‘sesquialtera’.

9 Coined from the ancient Greek triogdoolios, meaning ‘(in the ratio) of the whole and three-eighths (to the whole)’ (from treis, ‘three’, + ogdoos, ‘eighth’, + holos, ‘whole’), upon the model of ‘hemiola’.

10 Emmanuel Bach, Carl Phillip, Essay on the True Art of Playing Keyboard Instruments, tr. Mitchell, William J. (New York: W. W. Norton, 1948), pp. 87–99Google Scholar; Quantz, Johann Joachim, On Playing the Flute, tr. Reilly, Edward R., 2nd edition (London: Faber & Faber, 2001), pp. 91–100Google Scholar.

11 Bach, Essay on the True Art, pp. 87–99; Quantz, On Playing the Flute, pp. 91–100.